Known in the art is a catalyst which uses alumina as a carrier coat material and which carries silver oxide (for example, refer to Japanese Patent No. 2801423, Japanese Patent Publication No. 2008-240568, and Japanese Patent Publication No. 2009-160548). Such a silver-alumina-based catalyst absorbs the NO2 in the exhaust gas when the air-fuel ratio of the exhaust gas is leaner than a stoichiometric air-fuel ratio and releases the NO2 which was adsorbed when it becomes a set temperature. When the silver-alumina-based catalyst becomes the set temperature, the NOx catalyst which was arranged at the downstream side is activated and can purify by reduction the NO2 which flows out from the silver-alumina-based catalyst.